Melt the butter in a large Dutch oven or heavy-bottomed pot over medium heat. Add the chopped onion and cook until softened and translucent, about 5-7 minutes.

Add the sliced mushrooms to the pot. Increase the heat to medium-high and cook, stirring occasionally, until the mushrooms have released their liquid and started to brown nicely, about 10-12 minutes. Add the minced garlic during the last minute of cooking.

Sprinkle the gluten-free flour over the mushroom mixture. Stir constantly and cook for 1 minute to cook out the raw flour taste (creating a gluten-free roux).

Slowly whisk in the vegetable or chicken broth, ensuring no lumps form. Bring the mixture to a simmer, then reduce the heat to low, cover, and cook for 15 minutes to allow the flavors to meld.

Use an immersion blender to blend about half of the soup until creamy, leaving some texture from the sliced mushrooms. Alternatively, carefully transfer half of the soup to a standard blender, blend until smooth, and return to the pot.

Stir in the heavy cream, dried thyme, and gluten-free Worcestershire sauce. Heat gently until warmed through (do not boil after adding the cream). Season generously with salt and freshly ground black pepper to taste before serving hot.